An invariant structure is introduced in a decision model with continuous observations. Invariant and almost invariant decision rules are defined and related by a result of STEIN'S theorem type. Some topological properties of the space of invariant decision functions are established in order to prove the existence of an optimal invariant terminal decision function. Finally the problem of optimal invariant stopping is solved and the invariant estimation of the drift of a second order process is considered as an illustration of the method.